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QuestionMathematics

Triangle 1 has an angle that measures 62° and an angle that measures 14°. Triangle 2 has an angle that measures 14° and an angle that measures x°, where x ≠ 62°. Based on the information, Bob claims that triangle 1 and triangle 2 cannot be similar. What value of x, in degrees, will refute Bob’s claim?
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Answer

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Step 1:
Let's solve this step by step:

Step 2:
: Recall the angle sum property of triangles

- In any triangle, the sum of all interior angles must equal 180° - This means the third angle can be found by subtracting the known angles from 180°

Step 3:
: Calculate the third angle in Triangle 1

- Third angle: $$180° - (62° + 14°) = 104°
- Known angles: 62° and 14°

Step 4:
: Analyze the conditions for triangle similarity

- For triangles to be similar, they must have the same angle measurements - This means the corresponding angles must be equal

Step 5:
: Set up the equation for Triangle 2

- Third angle must be: $$180° - (14° + x°)
- Known angles: 14° and x°

Step 6:
: Set up the similarity condition

- For triangles to be similar, the corresponding angles must match - We want the third angle of Triangle 2 to equal 104°

Step 7:
: Solve for x

- $$x = 62°
- 180° - 14° - x° = 104°

Final Answer

62 degrees will refute Bob's claim, as this makes the triangles similar.